Solve for y
y=-\left(x^{2}+1\right)
x\neq -2
Solve for x (complex solution)
\left\{\begin{matrix}\\x=-i\sqrt{y+1}\text{, }&\text{unconditionally}\\x=i\sqrt{y+1}\text{, }&y\neq -5\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\sqrt{-y-1}\text{, }&y\neq -5\text{ and }y\leq -1\\x=\sqrt{-y-1}\text{, }&y\leq -1\end{matrix}\right.
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y=\frac{-\left(-x-2\right)\left(x^{2}+1\right)}{-x-2}
Extract the negative sign in x+2.
y=-\left(x^{2}+1\right)
Cancel out -x-2 in both numerator and denominator.
y=-x^{2}-1
To find the opposite of x^{2}+1, find the opposite of each term.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}